An Introduction to Financial Option Valuation Mathematics Stochastics and Computation 1 doc

... see (Iserles, 19 96; Mitchell and Griffiths, 19 80; Morton and Mayers, 19 94; Strikwerda, 19 89). The texts (Clewlow and Strickland, 19 98; Kwok, 19 98; Wilmott, 19 98; Wilmott et al., 19 95; Seydel, ... eliminating the W i +1 j terms in (24 .11 ), and the formula then reduces to W i j = p  W i +1 j +1 + (1 − p  )W i +1 j 1 , (24 .12 ) where p  = 1 2  1 + √ k(r/...

Ngày tải lên: 20/06/2014, 18:20

... Index dividends, 49, 18 2 double barrier option, 19 1 down -and- in call, 18 8, 18 9 down -and- in put, 19 0 down -and- out call, 18 7 18 9, 260–2 61, 265 down -and- out put, 19 0 drift, 54, 10 5, 19 8 efficient market ... neutrality, 11 5, 11 8 12 0, 14 4, 14 6, 15 1, 15 4, 16 3, 16 7, 18 0, 18 1, 19 4, 232 cash-or-nothing, 16 7 16 8 sample mean, 34, 48, 64, 14 1, 14 6...

Ngày tải lên: 20/06/2014, 18:20

... formulas 10 5 11 .1 Motivation 10 5 11 .2 Where is µ? 10 5 11 .3 Time dependency 10 6 11 .4 The big picture 10 6 11 .5 Change of variables 10 8 11 .6 Notes and references 11 1 11 .7 Program of Chapter 11 and walkthrough ... walkthrough 11 1 12 Risk neutrality 11 5 12 .1 Motivation 11 5 12 .2 Expected payoff 11 5 12 .3 Risk neutrality 11 6 12 .4 Notes and refer...

Ngày tải lên: 20/06/2014, 18:20

... DENNEY AND STEVEN GAINES (Denney and Gaines, 2000) 36 Computer simulation 0 0.5 1 0 0.5 1 1.5 10 00 samples 0 0.5 1 0 0.5 1 1.5 10 000 samples 0 0.5 1 0 0.5 1 1.5 10 0000 samples 0 0.5 1 0 0.5 1 1.5 10 00000 ... the U(0, 1) sample means and variances approach the true values 1 2 and 1 12 ≈ 0.0833 (recall Exercise 3.5) and the N(0, 1) sample means and vari...

Ngày tải lên: 20/06/2014, 18:20

... small, then e 1. 96σ √ t+(µ− 1 2 σ 2 )t ≈ e 1. 96σ √ t ≈ 1 − 1. 96σ √ t and e 1. 96σ √ t+(µ− 1 2 σ 2 )t ≈ e 1. 96σ √ t ≈ 1 + 1. 96σ √ t. So the confidence interval is approximately [S 0 (1 − 1. 96σ √ t), S 0 (1 ... way to compute a quantile–quantile plot, as seen in Figures 4.4, 4.6 and 5.3. It is listed in Figure 5.4. We use MATLAB’s N(0, 1) pseudo-random number gene...

Ngày tải lên: 20/06/2014, 18:20

... that C(S, t) in (8 .19 ) satisfies (8 .16 ), (8 .17 ) and (8 .18 ). [Hint: to deal with (8 .16 ), take the limit t → T − ,todeal with (8 .17 ) take the limit S → 0 + and to deal with (8 .18 ) take the limit ... (Bj ¨ ork, 19 98; Duffie, 20 01; Karatzas and Shreve, 19 98; Nielsen, 19 99; Øksendal, 19 98). It is possible to weaken the boundary conditions (8 .17 ) and (8 .18 ) in...

Ngày tải lên: 20/06/2014, 18:20

... this model, you had these numbers, 11 .7 Program of Chapter 11 and walkthrough 11 1 11 .6 Notes and references Colour versions of Figures 11 .3, 11 .4 and 11 .5 can be downloaded from this book’s website, ... zlabel(’C(S,t)’) Fig. 11 .6. Program of Chapter 11 : ch 11. m. PROGRAMMING EXERCISES P 11. 1. Edit ch 11. m so that it applies to a European put option, as in Figure 1...

Ngày tải lên: 20/06/2014, 18:20

... expect a M := 1 M M  i =1 X i (15 .1) 14 1 15 .6 Program of Chapter 15 and walkthrough 14 9 %CH15 Program for Chapter 15 % % Monte Carlo for a European put randn(’state’ ,10 0) %%%%%%%%%%% Problem and method ... the delta. 15 .2 Monte Carlo 14 3 10 1 10 2 10 3 10 4 10 5 10 6 10 0 .1 10 0.2 10 0.3 10 0.4 Num samples Sample mean Fig. 15 .1. Monte Carlo approx...

Ngày tải lên: 20/06/2014, 18:20

... Ae −r(T−t) . (17 .10 ) 17 .2.  Show that C cash (S, t) in (17 .4) satisfies (17 .1) , (17 .2) and (17 .3). 17 .3. Differentiate (17 .4) to establish (17 .5), (17 .6) and (17 .7). 17 .4. Using (17 .4) and (17 .10 ), ... practice 15 5 Table 16 .1. European put value approximations from binomial method Option value M = 10 0 1. 4 716 M = 200 1. 4762 M = 400 1. 4726 Blac...

Ngày tải lên: 20/06/2014, 18:20

... between 0. 01 and 0 .1 (1% and 10 % interest rates). It is not important in this book whether D(t) is measured in dollars, euros, or any other currency. 11 2.8 Program of Chapter 2 and walkthrough 19 0 ... 1. 4. Market values for IBM call and put options, for a range of strike prices and times to expiry. 2.6 Upper and lower bounds on option values 15 Region for C 0...

Ngày tải lên: 21/06/2014, 07:20